Hadwiger conjecture (combinatorial geometry): Difference between revisions

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{{Expert-subject|Electronics|date=March 2009}}


The heat dissipation in [[integrated circuits]] problem has gained an increasing interest in recent years due to the miniaturization of [[semiconductor]] devices. The temperature increase becomes relevant for cases of relatively small-cross-sections wires, because such temperature increase may affect the normal behavior of semiconductor devices.
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==Joule Heating==
[[Joule Heating]] is a predominant heat mechanism for heat generation in integrated circuits <ref name="test">T. Bechtold, E. V. Rudnyi and J. G Korvink, "Dynamic electro-thermal simulation of microsystems—a review," Journal of Micromechanics and Microengineering. vol. 15, pp. R17–R31, 2005</ref> and is an undesired effect.
 
==Propagation==
 
The governing equation of the physics of the problem to be analyzed is the heat diffusion equation. It relates the flux of heat in space, its variation in time and the generation of power.
 
:<math>\nabla\left(\kappa\nabla T\right)+g=\rho C\frac{\partial T}{\partial t}</math>
 
Where <math>\kappa</math> is the [[thermal conductivity]], <math>\rho</math> is the density of the medium, <math>C</math> is the specific heat
: <math>k=\frac{\kappa}{\rho C} \,</math>
the [[thermal diffusivity]] and <math>g</math> is the rate of heat generation per unit volume. Heat diffuses from the source following equation ([eq:diffusion]) and solution in an [[homogeneous]] medium of ([eq:diffusion]) has a [[Gaussian distribution]].
 
==See also==
*[[Thermal simulations for Integrated Circuits]]
 
==References==
<references/>
 
{{DEFAULTSORT:Heat Generation In Integrated Circuits}}
[[Category:Integrated circuits]]

Latest revision as of 18:01, 6 January 2015

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